On the construction of some symplectic P-stable additive Runge—Kutta methods
Duration: 48 mins 58 secs
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| Description: |
Zanna, A
Wednesday 11th December 2019 - 14:05 to 14:50 |
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| Created: | 2019-12-16 16:03 |
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| Collection: | Geometry, compatibility and structure preservation in computational differential equations |
| Publisher: | Isaac Newton Institute |
| Copyright: | Zanna, A |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 4:3 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | Symplectic partitioned Runge–Kutta methods can be obtained from a variational formulation treating all the terms in the Lagrangian with the same quadrature formula. We construct a family of symplectic methods allowing the use of different quadrature formula for different parts of the Lagrangian. In particular, we study a family of methods using Lobatto quadrature (with corresponding Lobatto IIIA-IIIB symplectic method) and Gauss–Legendre quadrature combined in an appropriate way. The resulting methods are similar to additive Runge-Kutta methods. The IMEX method, using the Verlet and IMR combination is a particular case of this family. The methods have the same favourable implicitness as the underlying Lobatto IIIA-IIIB pair. Differently from the Lobatto IIIA-IIIB, which are known not to be P-stable, we show that the new methods satisfy the requirements for P-stability. |
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